Temperature Equilibration due to Charge State Fluctuations in Dense Plasmas

The charge states of ions in dense plasmas fluctuate due to collisional ionization and recombination. Here, we show how, by modifying the ion interaction potential, these fluctuations can mediate energy exchange between the plasma electrons and ions. Moreover, we develop a theory for this novel electron-ion energy transfer mechanism. Calculations using a random walk approach for the fluctuations suggest that the energy exchange rate from charge state fluctuations could be comparable to direct electron-ion collisions. This mechanism is, however, predicted to exhibit a complex dependence on the temperature and ionization state of the plasma, which could contribute to our understanding of significant variation in experimental measurements of equilibration times.

Figure 1

Electron-ion energy transfer rate in hydrogen at liquid density, $\rho =0.07{\mathrm{g}\mathrm{cm}}^{-3}$ and with an ion temperature of $T_i=1\mathrm{eV}$. The rate due to charge state fluctuations is compared to the rate from direct interactions predicted by the Landau-Spitzer [16] and Fermi golden rule [17] approaches.

Figure 2

Upper: response functions for the electrons, ions, and charge state in hydrogen with $T_i=1\mathrm{eV}$, $T_e=10\mathrm{eV}$, and $n_e=1\times {10}^{22}{\mathrm{cm}}^{-3}$. The inset shows the charge state response function on a larger scale. Lower: products of the ion response function with the electron and charge state response functions.

Figure 3

Upper and middle: fluctuation size and decay times [i.e., the $A_i$ and ${\tau }_i$ of Eq. (14)] in solid-density carbon obtained from Monte Carlo simulations. The color scale denotes the correlation size, so that larger fluctuations are the most prominent. The insets show the fit to selected correlation functions, as used to obtain the size and decay rates. Lower: the corresponding charge state occupations.

Figure 4

Electron-ion energy transfer rates in solid-density carbon, comparing the rate due to charge fluctuations with different models for direct electron-ion collisions [15, 16, 17]. The ion temperature is $T_i=10\mathrm{eV}$.

Figure 5

Ratio of the charge fluctuation rate to the Landau-Spitzer rate in solid-density aluminum with hot ions and cooler electrons. The inset shows the occupation of the charge states as a function of electron temperature. This calculation uses the Debye IPD model [47], which more accurately predicts the pressure ionized $M$ shell expected in solid-density aluminum.